# How to describe the electrons defined by the following quantum numbers?

## n=3, l=0, ${m}_{l} = 0$ n=2, l=1 ${m}_{l} = 1$ Do I just have to say that it has for example one 3s orbital with 3 subshells or do I have to add other information as well? I am struggling a bit with this one. Thanks in advance.

Apr 10, 2018

Here's how you can do that.

#### Explanation:

You have values for three our of the four quantum numbers that we use to describe the location and the spin of an electron inside an atom.

• the principal quantum number, $n$
• the angular momentum quantum number, $l$
• the magnetic quantum number, ${m}_{l}$.

This means that in order to describe the electrons defined by these two incomplete quantum number sets, you must mention

• the energy shell in which the electron is located because you know the value of $n$
• the energy subshell in which you can find the electron because you know the value of $l$
• the orientation of the orbital in which the electron resides because you know the value of ${m}_{l}$

For the first set, you have

$n = 3 , l = 0 , {m}_{l} = 0$

This set describes an electron that

• is located in the third energy shell because $n = 3$
• is located in the $s$ subshell because $l = 0$
• is located in the $s$ orbital because ${m}_{l} = 0$

So for this first electron, you have the third energy shell, the $3 s$ subshell, and the $3 s$ orbital. You don't know the value of the spin quantum number, ${m}_{s}$, so you can't specify the spin of the electron.

For the second set, you have

$n = 2 , l = 1 , {m}_{l} = 1$

This time, the set describes an electron that

• is located in the second energy shell because $n = 2$
• is located in the $p$ subshell because $l = 1$
• is located in one of the three $p$ orbitals because ${m}_{l} = 1$

So for this electron, you have the second energy shell, the $2 p$ subshell, and one of the three $2 p$ orbitals, let's say $2 {p}_{x}$. Once again, you don't have the value of ${m}_{s}$, so you can't say anything about the spin of the electron.